Gradient Fade on this texture in cycles
This can be done quite a number of different ways, I have listed three.

You could make a new UV map, and rotate the uvs 90° (like chebhou said). Then use that uv map just for the length fade.


You could add a Gradient Texture node (or a image of a gradient) and use a mapping node to control which way the gradient is going.


(my favorite) You could add a Texture Coordinate node and then a Separate XYZ node. That will give you a gradient running along the axis specified. In this picture it would be black at the left edge, and running along the X axis white at the right edge.




So your whole setup could look something like this. The X axis from the separate node is used for the "length fade." The Y axis is how I'm creating the beam fading out top to bottom. Then the Multiply node combines the two gradients.